Next week, the Houses of Parliament will host its first ever standup gig. It sounds like the set-up to a joke; surely the Commons has enough jokers already, boom boom. But Bob Marshall-Andrews MP, for one, is not amused. "It is not," he tells me, "very funny." Fair enough – I'm happy to defer to Marshall-Andrews, who is now the legislature's first ever comedy impresario, having booked the veteran comic Ivor Dembina to perform to an audience of peers and MPs on Monday.

It could be a tough gig for Dembina, who runs the Hampstead Comedy Club in London's leafy Primrose Hill. But he's used to tough gigs: his show, which is about the Arab-Israeli conflict, has attracted hate mail from Zionists. Entitled This is Not a Subject for Comedy, Dembina's "story with jokes" recounts his experiences as a peace worker on the West Bank (he has also performed the show there). This Is Not a Subject ... traces his evolution from Jewish boy raised to support Israel, to "one of those Jews", as he describes himself, "who believes we should give back the Occupied Territories, but hang on to New York."

By his own admission, this old-school leftie will make an unlikely guest in parliament. In advance of his Palace of Westminster debut, he is performing for free in a bar off the Charing Cross Road. The day I attend, the audience is about 15-strong, and one old gent asks Dembina to pause the show while he goes for a pee. Small wonder that Dembina – a modest 59-year-old with a London accent you could use as a crowbar – "can't help feeling a bit chuffed" about the parliamentary prestige. "I'm not bothered about being famous," he says, "but this invitation does seem like a reward for working very hard on this show."

Six years in development, the show is a labour of love for Dembina. It addresses his Hendon childhood, his rejection of his parents' politics, and his work with the International Solidarity Movement in Palestine, where he witnesses Israeli tanks bulldoze the house of a suicide bomber. "That's a family's home," Dembina tells a soldier. "Not any more, it isn't," the soldier wisecracks back. That remark represents a watershed moment for Dembina, a disciple of Jewish comedy who suddenly realises that Jewish comedy isn't very Jewish any more.

"Jewish comedy," he explains, "is part of our identity. But now it's stuck. Traditionally, Jewish comedy is warm-hearted, full of truth and intellectualism. But now, most people's perception of Jews relates to Israel, and Israel means tough. It's shoot first and ask questions later. And what's that got to do with vulnerability, with love of humanity? So Jewish comedy becomes just some dislocated tradition, like Scottish people tossing the caber." Dembina fills up. "I feel really sad. I really feel this loss."

Since volunteering in Palestine, and more so since making the show, Dembina has received letters branding him a "traitor" and a "self-hating Jew". But he's adamant that "I'm one of the growing number of Jewish people who want to speak out." He was invited to perform the show in Israel, where there is – contrary to many people's monolithic image of the country – a thriving peace movement. He also performed the show in the Occupied Territories, where audiences "were amazed that there should be Jewish peace volunteers", he says. "They found that very difficult to get to grips with."

Veteran Labour dissenter Marshall-Andrews visited Palestine, too – Gaza, in his case – on a recent parliamentary delegation. He thinks it's "enormously important" that anti-Zionist Jewish voices make themselves heard, because it "demonstrates that what Israel is doing is not done in the name of all Jews". But is comedy an appropriate way to make that point? Absolutely, says Marshall-Andrews. "There is humour in everything in life, however dire. I found that the Palestinians, although deeply oppressed, maintain precisely the humorous spirit that people often do in those circumstances. That side of the conflict needs to be shown."

Dembina goes further: jokes, he says, can change the world. His examples may be inauspicious: Reagan's killer quip in his 1984 debate with Walter Mondale ("I am not going to exploit, for political purposes, my opponent's youth and inexperience"); Vince Cable's recent "Mr Bean" gibe about the PM. But Dembina's belief that "comedy, like all art, can make points and influence people" has sustained him through the knotty process of creating this intimate show.

"I've always believed that comedy should be about things you care about and that affect you," he says. "But writing a standup show about this subject, I struggled with it for years." The invitation to parliament is a kind of vindication. "I just wanted to show that, if you give quality, serious-minded work to an audience, they will listen." And as for his new audience, "MPs and peers are no different from anybody else," says Dembina. "It's important for them to know that some Jewish people are deeply uncomfortable with Israel's behaviour. They need to be told."

•This Is Not a Subject for Comedy is at the Houses of Parliament on 22 March